volume 33, issue 1, P117-123 2004
DOI: 10.1007/s00454-004-1092-8
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Abstract: We consider a variation on the problem of determining the chromatic number of the Euclidean plane and define the ε-unit distance graph to be the graph whose vertices are the points of E 2 , in which two points are adjacent whenever their distance is within ε of 1. For certain values of ε we are able to show that the chromatic number is exactly 7. For some smaller values we show the chromatic number is at least 5. We offer a conjecture, with some supporting evidence, that for any ε > 0 the chromatic number is …

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